Question

one of the angles of a parallelogram is 150 degrees altitude drawn from the vertex of this angle if this altitude measure 6 cm and 8 cm find the perimeter of the parallelogram​

Answer 1

Given- ABCDis a parallelogram with ∠BAD=150  

 

Altitudes CF on AB and AE on DC are 6 cm and 8 cm respectively.

To find out- the perimeter of ABCD=?

Solution:  

Given that ∠BAD=150  

 

Since adjacent angles of a parallelogram are supplimentary, we get

∠ABC= 180    −∠BAD = 180  − 150  = 30  

 

Also CF=6 cm

∴  BC /CF  =sin30  

 

⇒BC = BC/  sin30  

=6/1/ 2  cm

=12 cm and AE=8 cm given.....(i)

Now arABCD= base × height =AB×CF = BC×AE

⇒AB= BC×AE  / CF

=12×8 / 6 cm =16 cm ....(from i)

∴ the perimeter (ABCD)=2(AB+BC)=2(16+12)cm=56 cm